Adaptive Finite Element Methods for Differential Equations

Adaptive Finite Element Methods for Differential Equations
Author :
Publisher : Birkhäuser
Total Pages : 216
Release :
ISBN-10 : 9783034876056
ISBN-13 : 303487605X
Rating : 4/5 (05X Downloads)

Book Synopsis Adaptive Finite Element Methods for Differential Equations by : Wolfgang Bangerth

Download or read book Adaptive Finite Element Methods for Differential Equations written by Wolfgang Bangerth and published by Birkhäuser. This book was released on 2013-11-11 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: These Lecture Notes have been compiled from the material presented by the second author in a lecture series ('Nachdiplomvorlesung') at the Department of Mathematics of the ETH Zurich during the summer term 2002. Concepts of 'self adaptivity' in the numerical solution of differential equations are discussed with emphasis on Galerkin finite element methods. The key issues are a posteriori er ror estimation and automatic mesh adaptation. Besides the traditional approach of energy-norm error control, a new duality-based technique, the Dual Weighted Residual method (or shortly D WR method) for goal-oriented error estimation is discussed in detail. This method aims at economical computation of arbitrary quantities of physical interest by properly adapting the computational mesh. This is typically required in the design cycles of technical applications. For example, the drag coefficient of a body immersed in a viscous flow is computed, then it is minimized by varying certain control parameters, and finally the stability of the resulting flow is investigated by solving an eigenvalue problem. 'Goal-oriented' adaptivity is designed to achieve these tasks with minimal cost. The basics of the DWR method and various of its applications are described in the following survey articles: R. Rannacher [114], Error control in finite element computations. In: Proc. of Summer School Error Control and Adaptivity in Scientific Computing (H. Bulgak and C. Zenger, eds), pp. 247-278. Kluwer Academic Publishers, 1998. M. Braack and R. Rannacher [42], Adaptive finite element methods for low Mach-number flows with chemical reactions.


Adaptive Finite Element Methods for Differential Equations Related Books

Adaptive Finite Element Methods for Differential Equations
Language: en
Pages: 216
Authors: Wolfgang Bangerth
Categories: Mathematics
Type: BOOK - Published: 2013-11-11 - Publisher: Birkhäuser

GET EBOOK

These Lecture Notes have been compiled from the material presented by the second author in a lecture series ('Nachdiplomvorlesung') at the Department of Mathema
Multiscale, Nonlinear and Adaptive Approximation
Language: en
Pages: 0
Authors: Ronald DeVore
Categories: Mathematics
Type: BOOK - Published: 2014-12-04 - Publisher: Springer

GET EBOOK

. . . . . . . . . . . . . . . . . . . 7 7 Hyperbolic partial differential equations and conservation laws . . . 8 8 Engineering collaborations . . . . . . . . .
Automated Solution of Differential Equations by the Finite Element Method
Language: en
Pages: 723
Authors: Anders Logg
Categories: Computers
Type: BOOK - Published: 2012-02-24 - Publisher: Springer Science & Business Media

GET EBOOK

This book is a tutorial written by researchers and developers behind the FEniCS Project and explores an advanced, expressive approach to the development of math
Finite Element Methods for Integrodifferential Equations
Language: en
Pages: 294
Authors: Chuanmiao Chen
Categories: Mathematics
Type: BOOK - Published: 1998 - Publisher: World Scientific

GET EBOOK

Recently, there has appeared a new type of evaluating partial differential equations with Volterra integral operators in various practical areas. Such equations
The Mathematical Theory of Finite Element Methods
Language: en
Pages: 369
Authors: Susanne Brenner
Categories: Mathematics
Type: BOOK - Published: 2013-03-14 - Publisher: Springer Science & Business Media

GET EBOOK

A rigorous and thorough mathematical introduction to the subject; A clear and concise treatment of modern fast solution techniques such as multigrid and domain